A Test for Comparing Multiple Misspecified Conditional Interval Models ∗

This paper introduces a test for the comparison of multiple misspecifed conditional interval models, for the case of dependent observations. Model accuracy is measured using a distributional analog of mean square error, in which the squared (approximation) error associated with a given model, say model i, for the interval [u, u] is measured by E (( (F1(u|Z, θ† 1)− F1(u|Z, θ† 1))− (F0(u|Z, θ0)− F0(u|Z, θ0)) )2) , where Z is the conditioning information set, F1 is the distribution function of a particular candidate model, and F0 is the true (unkown) distribution function. When comparing more than two models, a “benchmark” model is specified, and the test is constructed along the lines of the “reality check” of White (2000). Valid asymptotic critical values are obtained via a version of the block bootstrap which properly captures the effect of parameter estimation error. The results of a small Monte Carlo experiment indicate that the test does not have unreasonable finite sample properties, given very small samples of 60 and 120 observations, although the results do suggest that larger samples should likely be used in empirical applications of the test. JEL classification: C22, C52.